Sometimes people say that water is r+ ghpzlb 82a:1w3iu elemoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statewl8gl 31a+2hzup i:e bment?

Will the acceleration oz-4f* o.gb3u g fj5vcsf a car be the same when the car travels around a sharp curve j g3 g5vz4fb.o-scfu* at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r-uh(rt t u:vglg942kcoad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a h :vgl9kg(utht4-ru2 cill?

Describe all the forces acting on a child3 1q x/wz0oh2zlhfnnb,0xq3a riding a horse on a merry-go-round. Which of these forceb1hw,f z l/0xo0zxqn2ha3q 3ns provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circp,ikspw,/ 2dr tc+a 55fkba.x a )(uzdle without the water spilling out, even at the top of the circlep +,2)a c(r5,dxuibsa pa/ t5kfkwdz. when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There 83e3yugmsck1s spx/ 1are at least three controls in the car which can be used to cause the car to ac3syum c 11gse38skx /pcelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sma86ewm/sdu6 a rll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s secon6/se rdmau68w d law.

Why do bicycle riders lean inward when rounding a curhuu.fq o:)c*f9 v 2nrwve at high speed?

Why do airplanes bank when they turn? How womuog .)/5et-..q pl) grcbhi:wqd mc7 uld you compute the banking angle given its speed and radius of the hbdwp)m u5 o)l.g .ireccm:-tqg7/q.turn?

A girl is whirling a ball on a string around her heo*mx3eft u/ 9.e5uykr 0nux3had in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?ht m93ufken. uexy*o 0u/x3r5

Does an apple exert a gravitatimj7kb2zxbdxr*h.n .n h 5,fk 2onal force on the Earth? If so, how large a force? Consifdb7jn.nb*m hk. x, xzh22kr5der an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s ybpk.rl, jctaj2 udj)0-dg(p(9h 6i jorbit dck2j j(jdlp( r0)9by.p-g,a 6ijh tube different?

Which pulls harder gravitationally, the Earth on the Moon, or .+p3dcw ; h8(lwuwwgr the Moon on the Earth? pcdw3.+;hglrw( 8wu w Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet1vsla2jpus/; the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earthj1lvs; sp2 a/u to the other.]

Will an object weigh more at the equator or u1br9d7b3tqyuo4gq* 8 we9uz at the poles? What two effects are at q39uq8 weot4d19gzb 7uuy*br work? Do they oppose each other?

The gravitational force on the Moon due j*fnw c0gxpguz8hy. 7mhg 9udh ):;+d to the Earth is only about half the force on thec79jgxhh*pgnu.z+ hmy;gdf0 8)du w : Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in it d 1:a-epa 8uvk;jj5zys orbit around the Sun larger or smaller than the centripetal acceleration of the Eart8j5yd 1 e;pazakjuv:-h?

Would it require less nx3p;-+du gncnnfw qs8:h 3( aspeed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotanfgn(nq + xcdhn8u3a;wps -:3tion direction.

When will your apparent weight be the greatest, as measured by a scale in a movtqv .sa.+-mx,bo5nc b ing elevator: when the elevator (a) accelerates downward, (b) accelerates upwc t.,omb-+.qb5xan vsard, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long pek3 wwhd g4k09i/ i(xgcriods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walck30 g ikdh94iw(g/ wxking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner exper/ (w.+pxec(arswe lg s1/*reyiences “free fall” or “apparent weightlessness” betweep*w/ex c/(r(.e y+gelwss r1an steps.

The Earth moves faster in its orbit around the Sb.,2 r azbh,iaun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This i.a z,bh2arb i,s not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discoveaf j);bw rnk xkkuf:x 1k9zl -80ld4*nred to have a moon. Explain how this discovxdk*f)zx k; abu 8fll1k4-n9n: w0 kjrery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the E,+k4jme6xd 3jv a)uhl arth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differ v)3ml4je+kha dj6ux, ence in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 15,gwqbk.0es ) n;cxr ulj5fo1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its o.qahz)b yf /;irbit around the Sun, and the net force exerted on the Earth. Whf/ ziqhya;.) bat exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotate3-5 q*cxs: tm7de 9k htno)sers uniformly in a horizontal circle (at arm’s length) of radius 0.90dh9n qxk:oer)et c m*57s -3ts m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's suw3 nqr ulb;e7,1 cjh90vpo dg:rface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleratiov;91u,pc7obg l3he j:rwd nq0n at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay od0x/vz)ud:v1.fb-yy ku a0 *nur 0exi n the edge of a potter’s wheel turning at 45 rpufz/ay v0y u):bu-e0d1d.kx*rv0 nxim (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circl;vt exjqk+ 3-(ols iu;e of radiuu(e 3qv+; lxtko; -jsis 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speedk d+ iryq gr)hk5+u 0/tlp d :tnx9sp**wj4c7i with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static fricwp t5h)qrdil*dg p0kr94:+y /ut jc*nsi k +7xtion between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frictcb. c lum938 wv9 wqw,o3l/nztion be between the tires and the road if a car is to round a level curve of radius 85 m at a spzmt qw/lo99c,8wn. l vc b33uweed of 95km/h ?   

  A device for training astronauts and jet fighter pilots iszpsh .6*i kz/g)tmcyl4r4 t +v designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotatin+ lm)c4/h6tg4yvi.*zt zs pk rg?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable l6kb h ;ip4ws*speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is lwp4;k6bs*h ithe coefficient of static friction between the coin and the turntable?   

  At what minimum speed must hzwgeo(u. /*wa roller coaster be traveling when upside down at the top of a circle hzowuw(/ .*ge
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses t4b/oyg83 mjel t 6d1arhe rounded top of a hill (etyj/ 8g6m4a1ro d3lb radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m- *tj;wyi0 eot4diameter Ferris wheel need to make for the pass*y4 ew;oj0t tiengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cirasob8 *shy89t cle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportinbo hs *t89ys8ag the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from the axis ol z:j) fucv9i, m7mzj:f rotation is to experience an acceleration of 115,00,c:zmimv 9 ujfz:j)l 70 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivgswcypq.q f959z7k s* tb,v:ial, people are rotated in a cylindrically walled "roo,*wv7gs959y ci :zqptsk fq.bm." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circlek4qd8hc gz 98v on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to aczdv8q9 gh48 k dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , prec te e8a5i,ruu*isely this time, by not ignoring the weight of the ball w8,5aieture * uhich revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is p3b 8ava sj2jfmg(m*3m7 k otv0erfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses fmyqy4*n zy-f55pdu* $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuve he4)2qd duvj5u7 9meir by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal componenf 0/p fium8aia6 s -.6ykt0;jnp.nbiz )b6xjt ts of the net force exerted on the car (by the ground) in E0 )6bt0.za k8/.s;6yi6nu x tiijfa nbfpj m-pxample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, going 1utfgehzz8 e.l31;i k from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it .hzluzt8e ; e1f1g3ikis halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partidtr0hko7t3r/8yb5 ov cular instant 7k8r/o vy5 3thr0bodt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rkm vs8sjz7kzmz7p7.xgm e5(7 q-* tuyadii) above mqp7 zx57 (mtk7 8yssz* .mjvu ezg7-kthe Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a macssdy* p2o xig4;i99s gnitude of 12 29idx9* s cposg 4syi;m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. Th: 1kyu.fhlc/1 xph vfoho4 o8.e Moon's radius is 1.74 l.kho c v1h.ff:4po1h o/uxy8$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tid7 1h b 2byr(p,gtvwf9z;t x)hmes that of Earth, but has the same mass. Whbzhfx97w)h t;t2(p ,v g r1dybat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ec br( a46 mvgwp z3l337eik4aearth, but the same radius. What i4 47lr 3pba c3wa3gmez6(i evks g near its surface?   

  Two objects attract each other grafr0o-jy.jwle2k s *, pmsp,9,m y*d ywvitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g ,.8pl ) :uf/u:up1uud z3i*w jmku+hjd the acceleration of gravity, at (a) 3200 muj:mdzk f) p+wi83ul:h dp* uuu/j1.u    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earts; pc z1et x;h-/m: d8nl. mrovlmv1m4h where thegravitational acc;mvnmpez48 1;mtl1rh sm/:lx d . o-vceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packdyj 7:2ug,l b zd- v2lykz-d6sed into a sphere about 10 km in rad v22g-z-7j s,ky6ydludzdl: bius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun buy)1jr c.jv v w8;szp:xt is now in the last stage of its evolution, is the size of our Moon but has p);:1vsc zjr8 jwvyx. the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while r)/sb0budo o,nr: g6hqf0k;qorbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince th k :0 ;fqrb,urod0/no b6qh)sgem and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calc; pkd fwng(n+.ulate the magnitude and direction of the total gravitational forc+knp g .wdf(;ne exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pp/ yjs5-rk9qjf/gv r9lanets line up on the same side of the Sun. Calculate the total force on the Earth due to krgp5qsr9v//fy-j 9jVenus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 ojy3c n2lm (az5f what it is on Earth, and that Mars’ radius is 3400( la23mnyjzc 5 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kn jb1hrk2s.( 34,i,im om:t ngggt 5iapown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawsgm( g15t pisb34,. i2ntjrok,miah:g, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular osdaoa 44ak v 3++an4ols,jok1 e+s:nf rbit about the Earth at a height of ndo4lk + 4k:+1jf ovsassna+e4, oaa3 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular oj08/f0ef suylkbc t03rbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ek 3/00 uc0fftbjey8slarth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants axzffm :8lvo (2re to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give you(o:ffx vm2z 8lr answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite tfxf :-gc 03y, qsuv1gvo orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the sat3guf cvf1:- ,sx q0vygellite?    s ~    min

  At what horizontal velocity woulda ;gqfb,m) a.z a satellite have to be launched from the top of Mtbqg,z fm)a ;.a. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the col43*i uv: :6f;wne0z prxjqhummand module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around thw iznl :f0xq6 pur*ju;4 ev:3he Moon once?    s

  The rings of Saturn are composed of c ct6y /ayiw1g kfx4f76hunks of ice that orbit the planet. The inner radiusty/x741 cf 6iwa6fgky of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates onjhis/g*/y+oa)7xajmuq1a9a 7 s -l ejce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to heq y 7iao1)eajjhj9/ /m sgua-7x+l as*r real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the 3vhp x s5i 0v40u 8*dpuxwduj.center of the Earth's Moon in a space vehicle (a) moving at constant velp i jxv4u8305vhdpx*dw.uu0 socity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of tw pi0ddi d3f 78sd+u3nno stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway bi n0 f i38d73npddu+dsetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevatoroi kca,4d6 2*vc5 qp6bzs/c jf/t+tml that mov6 ist*fl+5k d /ao,cptcq2v j 4mzc/6bes
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord su *-yz n-nd3aegspended from the ceiling of an elevator. The cord can withstand a tens*yn3-nd g-eaz ion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near5y3uuv r3w epx2g(ho zg40bb 0 the surface of a planet with period T , the density (3ey(vg0u bu0 br45 hgp3wzx2o mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period ofi;ydy,kevk-55 nm5*k 5qqx us an artificial satellite o5nv5ksduyk5i; * xqkm 5,-eqy rbiting very near the Earth’s surface.    s

  The asteroid Icarus, thjlwio65n6 m- d zhm:*uough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What uwio-n6zh:d6*jm lm5is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanceg )0ey/fsr gby q92jfgm kty) 0jl2l3. of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every klt akk:ax+t5srsu i0p ad;.pn 1 *(y676 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is neaxnp r6 lta01 5udaktk+s(:*y ;ips.akrest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce rtl3 k70i2y*jp6 jblsnter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mooxt jpx9 8fou ljr+8d/)ns of Juu8)rx j9+8x jt/fd lpopiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the know )5*i g jyc*r,6ymavign period and distance of the Moon. y*r*av g6g iycj5)i,m    $\times 10^{24}$

  Determine the mean distance from Jupiter for each6 e28wobj9sfhbqz /n lt6 ak4t 4;lr5e of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the perst5re afh 2 l4jwb;9kl86 no46etzb/qiods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of)whurs9 ld2s d b2(8oi many fragments (which some space scientists think caid9ursh dlwb2 ()2s8 ome from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an fmyx + -b+wz0uartificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine tb+xu+zw- y0fmhat this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge byd5qra7z.yz p 1 swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he ca 7qaprz1d.y5z n tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what4emb ,j4;g-xk af c1a:tfdz7 x it is on the surfaceae;fm 44tfbzx 7c:1k djx-ga,?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mu8e oc*pllh 0p0tual circle once every 2.5 s. If we assume 0 l8oh0lppec *their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once peqe 8ilk9 97djqik;i+hr day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. 9e;q 8jil9hiik +7dkqWhat fraction of g is this?    $\times 10^{-1}$

  At what distance from the jqs esz*+ny8qfr4yy/*1u p0tEarth will a spacecraft traveling directly from the Earth to the Moon experience zer1sq4j ey8tq snr**z0/f py u+yo net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom s9s.h a -oej3z tm:vqnr60-sndcale in an elevato0-6sdn3sa 9.nteo z:-vrj mq hr, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c js3o5,rvt+tg onsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). +sto5,t rjgv3The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). bmdlg44:xd/ n(rcgf3ad1q w8kcw+t8
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms o 2namp -ky3ot:pf28 sxf its radius r, the acceleration due to gravity at its stoyp8 a:m s23-fx2k npurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) i64bat/+h(txi7le fd5p qs- e hs deflected from the vertical by ands-tx 7pli6h t/5e4b+hf aq( e angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 675j(gh 1g 5 mp8az yvew4/es6jl m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what 1lw mz5 pyj(ej4/gg5v s 6ha8erange of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast l1 mz.kwg f2,2 a*adci (d+vwtthat objects at the eq*ai + fk2ag,12wd tm(c w.lvzduator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 t(xb 77yk-y)l* ihxig$\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rcp 68gawnb77n7sm dr id 7m5gvbyf2.6ounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to m ggfn6c 7 irbyw 25 dn.sa7d68mbp7v7an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed ty6xta ,hmr02nl 9 ;d,o.ibsz that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would9sz oxm., bt; at d2nrhi,0yl6 experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telesi 4;)oiz 1xexrgg2g8ucope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thisx z g48)igx;reigou2 1 by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill ak/k unfxxui 5jn;h.4ip1 v.m(nd valley shown in Fig. 5–45. Both the hill and valley4hu(1un.;x xmk f /jk5p. nivi have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Po l08 (gd(ll sg0.: l2vs5 jggfgb/j lhy:uurl1sitioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,g:ufrgs0(/(:521 ull0 8yblg vgl h l.jslgjd000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, i)n a9asn9xfh1s meant to orbit the asteroid Eros at a height of about 15 km . Eros is ron 9xa1hns9)a fughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space axz+:qgvc+014d2/naz f nnrw shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius asanz :/aw+z n+c21 n4 0rdfgxqv the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its ) kjn,yow/jxmx-d 08wmean distance from the Sun?n /yo8xmxw0-, j )dkwj   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value +c6.ewl8s n d ax23jvv+*njlaof G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you.x3 jn+n8s.d6w+lla 2ac vv *je Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy5z:yxb8cl*lx v) )sq b (Fig. 5-46) at a distance of about 30,000 light-years from*sb q)ylb z)5x 8cv:lx the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.a:rxgxpn8uda-.6 o)8p b g j6 /vvnjb 09+mknt50 m on each side. Find the magnitude and direction of the gravitational force on a fifth o pmd)b:-gvn9 6 x0/nb. ajk8n68 apr vjgt+ux1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits tgopl :x:7xdgn (,;wrt he Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by 77s .t vjggsmip,ip3 +the tip of the 1.5-cm-long sweep second hand on your wrv7+3.p,mg ss gj p7tiiist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around i0i gy9h:cmwh/ vt ft/*8)owgjn a circle below you on a 0.25-m piece of fishing line. The weight makegcyjw v80g:) *h/ift tm/ ohw9s a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designede (d-5ja0 q+ihed/:g;crt vf)pcsc:g so that a car traveling at spvg pjctdf ;5das(e e)c+hc 0/gir- ::qeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whwry.qd9uwp k4d/wi4bx g+ )x- en negotiating curves. The angle of tilt is adjusted so that p4yg-k x9 .b4 wwdiwxu/q +rd)the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$